Suppose X is a normal random variable with mean 𝜇 = 70 and standard deviation 𝜎 = 5. Find a such that P(X ≥ a) = 0.01

Question

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Suppose X is a normal random variable with mean 𝜇 = 70 and standard deviation 𝜎 = 5. Find a such that P(X ≥ a) = 0.01. (Round your answer to one decimal place.)

a =

Answer 1

z score z=2.33 has probability 0.01, according to on line z tables

zs = z score times standard deviation = 2.33(5) = 11.65

70+11.65 = 81.65

Pr(X>81.65) = 0.01

rounding is usually up to the next digit, if 5 or more, so you'd probably want 81.7

but 81.65 was a little imprecise, as z tables are already rounding off a little. 81.6 might be more accurate.